
While computing \(\Delta {\bar{\mathbf {q}}}\)  is feasible via
Eq. REF , obtaining the relative position term
\(\Delta {\mathbf {p}}\)  requires \(^{I(t_k)} {\mathbf {v}}_{I}(t_{k})\)  and \({^{I(t_k)}}{\mathbf {g}} = {^G_I \mathbf {R}^T}(t_k) {^G\mathbf {g}}\)  from Eq. .
If a DNN method is able to compute \(\Delta {\mathbf {p}}\)  by using windowed IMU measurements, this network must also obtain \(^{I(t_k)} {\mathbf {v}}_{I}(t_{k})\)  and \({^{I(t_k)}}{\mathbf {g}}\)  as hidden variables. However, both terms are not necessarily observable using IMU measurements [1]}, unless patterned motion [2]}, zero velocity event [3]}, or other special cases are involved. In other words, it is always possible that under the same IMU measurements the corresponding position (\(\Delta {\mathbf {p}}\) ) is different.
